Medical diagnostic systems (Orvosbiolσgiai kιpalkotσ rendszerek) Elastography (Elasztogrαfia) Miklσs Gyφngy Motivation [Konofagou 2004] • Palpation (stiffness measurement by hand) used for centuries by doctors to detect abnormal tissue • Example: cancer stiffness >> healthy tissue stiffness • However, palpation is qualitative and can only detect stiffness changes at skin surface • For example, breast self-examination often leads to misdiagnosis and is no longer recommended [Baxter et al. 2001] Aim • method of inducing and measuring displacements deep within tissue • estimate stiffness quantitatively, using a measure such as Young’s modulus (E), shear modulus (G), bulk modulus (K), Poisson’s ratio (.) • avoid image artefacts like speckle Another motivation: HIFU [Gyφngy 2010] • High intensity focused ultrasound (HIFU) is a technique to noninvasively destroy tumours by thermal and mechanical means [Kennedy 2005] • Thermal ablation by HIFU (or indeed ablation by other methods such as RF) causes marked change in stiffness • Elastography suggested as a method of monitoring HIFU • In many of the applications mentioned in this lecture, HIFU ablation was used as a method to cause lesions • This demonstrates the applicability of elastography to monitoring HIFU treatment (though sometimes HIFU creates interference) • Moreover, HIFU exposure/treatment provides a great “testing platform” for novel elastography methods due to the marked and localised change in stiffness Overview of this lecture • Theory • viscoelasticity • shear and compressional waves • Applications • quasi-static elastography • vibration amplitude elastography • acoustic radiation force impulse imaging • vibroacoustography • harmonic motion imaging • supersonic shear wave imaging • MR elastography • pulse wave velocity Medical diagnostic systems – Elastography Modelling tissue viscoelasticity • What happens if tissue is put between two plates and compressed? • Elastic material (spring model): . = E. • Viscous material (dashpot model): . = .(d./dt) • Tissue both elastic and viscous (viscoelastic) • Connectin, elastin, cytoskeleton and other fibrils (inside and outside cell) give elasticity • Friction of fibers and cells sliding past each other (sometimes increased by cadherin proteins linking them together) provide viscosity [Foty and Steinberg 2005] • How do elasticity and viscosity combine? . “Layer of epithelial cells.” Edinburgh University and Wellcome Images. Creative Commons License. http://images.wellcome.ac.uk/ B0003763 nuclei cytoskeleton cell-cell adhesion molecules “Cultured endothelial cells.” Denise Stenzel, LRI, CRUK, Wellcome Images. Creative Commons License. http://images.wellcome.ac.uk/ B0006773 Viscoelastic tissue models [Gao et al. 1996; Hill et al. 2004, pp. 100-105] • Maxwell: tissue keeps shrinking on application of constant stress (creep). Energy dissipation (absorption coefficient .a) decreases with frequency. • Voigt: viscous resistance decreases with decreasing velocity, .=-./E(d./dt)+.(d./dt) causing exponential shrinkage towards the inviscid case (if stress suddenly released, tissue also relaxes in exponential fashion). .a~f 2 as f›. • Time causal: [Szabo 2004, pp. 91-92] dashpot in Voigt Maxwell model replaced by arbitrary response function • Kelvin/Zener: dashpots in series and parallel with spring. Peak . = E. + .(d./dt) in attenuation for some frequency. • Multiple relaxation: multiple Kelvin elements cause broad attenuation response with frequency • Kelvin-Voigt fractional derivative: [Kiss et al. 2004] Voigt model differential operators of fractional powers Viscosity vs. elasticity [Hill et al. 2004, pp. 102-103; Kiss et al. 2004] • Strain response to stress due to viscous and elastic elements eqvt. to charge response to voltage in circuit with resistors and capacitors • Consider Voigt model (eqvt. to resistor and capacitor in series): . = E. + .d./dt • Taking Fourier transform: .F/.F= E(1 + j..) (complex elastic modulus) where .=./E (response or relaxation time) . = 1/. is relaxation frequency (cf. cutoff frequency in electronics) • Voigt model does not capture tissue response adequately • However, it does correctly predict that as frequency is increased strain gets increasingly out of phase with stress, resulting in absorption • It also demonstrates that dynamic loading/unloading of tissue can be used to recover not only elasticity, but also viscosity of tissue [Catheline et al. 2004] • Substitution into wave equation yields .a~f 2 [Catheline et al. 2004; Raichel 1972] (cf. classical [Stokes 1851] thermoviscous formulation [Lighthill 2005; Szabo 1994]) Compression vs. shear • Both (bulk) compression and shear have elastic and viscous constants • For tissue, bulk modulus K . 104 Χ shear elastic modulus G • Hence, since cC =.(C/.), cK . 102cG (1500 m/s vs. 15 m/s) • At 1 MHz, this means wavelengths of 1.5 mm vs. 1.5 ΅m • Also, at low frequencies (~100 Hz), shear waves dominate, since the low value of G provides a much greater compliance to displacement • Thus, tissue is relatively incompressible (..0.5): G . E/3 [Parker et al. 2005] (see also http://en.wikipedia.org/wiki/Elastic_moduli for elastic moduli equations) • Hence, (real component of) elasticity measured by assessing quasi-static or low-frequency displacements is mostly due to shear modulus G • On the other hand, the shear wave equation is such that the wave amplitude decays by e2. (.535) every wavelength, so that at ultrasonic frequencies shear waves only propagate on the order of micrometers [Cobbold 2007, pp. 86-87] Shear modulus and waves [Cobbold 2007, pp. 568-571] • A map of shear modulus G provides much higher contrast (and thus differentiation) between different tissues than bulk modulus K • Using external or localised displacements, either measure resulting strain OR observe speed of resulting shear wave to infer G (=.cG 2) • Thus, promise of quantitative, high contrast and speckle-free images when compared to B-mode imaging (where contrast is due to changes in K, .) liquids bone soft tissue breast dermis, epidermis, bone glandular connective cartilage tissue, tissue, liver, fat, contracted relaxed muscle, muscle palpable nodules Comparison of shear and bulk moduli. Adapted from [Sarvazyan et al. 1998]. Elastography – approaches [Gao et al. 1996; Parker et al. 2005] • Quasi-static compressions (<5 Hz) – tissue has time to relax (purely elastic term) – variation so slow that wave phenomenon not observable over sample – external palpation: free-hand compression with array OR mechanical vibrator – passive palpation: organ (e.g. motion of lungs or heart) • Periodic or transient compressions – shear waves propagating from boundary such as skin (vibration amplitude elastography) OR shear waves generated locally in tissue (remote palpation using acoustic radiation force impulse imaging, vibroacoustography, harmonic motion imaging, supersonic shear wave imaging) – information about dynamic properties (e.g. viscosity) • Elastography not exclusively ultrasound technology (MR, PVW) Quasi-static elastography • Apply external force • Estimate localized displacements using cross-correlation methods • Unknown stress field • Difficult to obtain quantitative data • See [Righetti et al. 1999] for examples of quasi-static elastograms Vibration amplitude elastography [Gao et al. 1996] • Vibrator placed next to ultrasonic probe generaties shear waves into sample • Vibration of scatterers causes spectral shifting of the echo • The spectral shift can be detected using Doppler imaging • Spectral shift variance proportional to vibration amplitude • Infer elastic properties from vibration amplitude • Note also: wavelength of shear wave at e.g. 200 Hz is ~ 5 cm • Phase and amplitude maps allow visualisation of wave propagation with time • Gradient of phase and amplitude in direction of wave propagation allow estimates for local shear wave speed and thus shear modulus G • See [Gao et al. 1996] for illustrations Acoustic radiation force impulse (ARFI) imaging [Fahey et al. 2004; Nightingale et al. 2001; Nightingale et al. 2003] • Acoustic radiation force (ARF) nonlinear phenomenon dependent on attenuation coefficient ., acoustic intensity I and speed of sound c ARF= Wabsorbed/c =2.I/c [Fahey et al. 2004] local strain . local stiffness Χ local ARF • ~30 ΅s pulses (pushing beams) focussed at various region of interest • One pre-ARF pulse-echo; several post-ARF insonation to track temporal response • Possibility of estimating shear modulus from propagation speed of displacement • Illustrative example [Fahey et al. 2004]: • Liver sample injectied with formaldehyde • Area around injection expected to stiffen within minutes due to protein cross-linking • B-mode: subtle increase in echogenicity observed around affected area • ARFI image: affected area shows less displacement due to ARFI, ie tissue has stiffened • ARFI image shows much higher contrast Vibroacoustography [Alizad et al. 2006; Alizad et al. 2008] • Similar in principle to ARFI imaging in that localised ARF is generated • However, here the localised ARF is generated using two overlapping beams of slightly different frequencies (e.g. 3000±15 kHz) • ARF is ultrasonic: (high-speed) compressional rather than shear waves generated • Hence, displacement amplitude/propagation cannot be tracked • Instead, amplitude of emission recorded using hydrophone (receiver matched to water) • Illustrative example [Alizad et al. 2008]: – Examining calcifications in an excised human prostate – X-ray (traditional method to detect calcifications) and vibro-acoustogram both detect calcifications with excellent contrast – Calcification nowhere to be seen on B-mode! Harmonic motion imaging [Maleke and Konofagou 2008] • Stems from vibro-acoustography: generate localised harmonic motion • However, as of late, local vibrations are not induced by two overlapping beams (as in vibro-acoustography), but by amplitude-modulated (AM) ultrasound insonation • Also, vibration frequency is lower (10–40 Hz) and tracked using cross-correlation of RF A-lines • More complex than recording with a (cheap) hydrophone, but also potential for more quantitative information • Viscous component estimated from phase information [Vappou et al. 2009] So far on the remote palpation channel... ... we’ve been watching the generation of an acoustic radiation force at some location To provide a map of stiffness over a region of interest • location of “virtual finger” needed to be scanned (reducing the frame rate) OR • (if applicable) speed of shear wave emanating from pushing location was estimated (shear wave quickly attenuates and several pushing locations were still needed) Towards supersonic shear imaging – some preliminary observations • compressional waves much faster than shear waves that they generate • as a consequence, a pushing location can be set up “instantaneously” compared to the slowness of the shear wave • what if several pushing beams were generated in quick succession to generate a wavefront? Supersonic shear wave imaging [Bercoff et al. 2004] • Special case of shear wave velocimetry • Series of pushing beams synthesised deeper and deeper in tissue, at a scanning speed of cS • Wavefront produced propagates at shear wave speed cG • E.g. (cG, cS) =(2,6) m/s, Mach cone (Mach 3) produced • Propagation of Mach cone imaged at 3 kHz to provide map of shear modulus Advantages over ARFI: • entire plane can be imaged in one fast sequence of pushing beams • high frame rate of images • less chance of thermal or mechanical damage to tissue MR Elastography • Elastography measures mechanical properties • Although displacements may be generated by (ultra)sonic transducer, imaging of displacement not limtied to ultrasound! • Displacements due to static or periodic compressions can be imaged using other modalities (e.g. MR!) Illustrative example: [Larrat et al. 2010] • MR elastography monitoring experimental HIFU surgery of a restrained rat • 400 Hz piezoelectric transducer is placed at the head of the rat, generating motion inside the brain • motion-sensitive gradient (MSG) MR pulse sequence used to measure motion Pulse wave velocity (PWV) [Boutouyrie et al. 2009; Segers et al. 2009] • Cardiovascular disease is a major health problem worlwide • Arterial stiffness correlates strongly with cardiovascular health • As in other forms of wave propagation (e.g. bulk compression, bulk shear), velocity of propagation along vessel is proportional to the square-root of a relevant elastic modulus: PWV = .(Eh/.D) (~10m/s) (E: Young’s modulus; h: wall thickness; .: blood density; D: vessel diameter) • The wave itself is initiated by the heart during systole and is reflected back to the heart when the wave encounters an arterial branching point • This reflections allows estimation of the PWV on an ECG (as well as being a source of worry if it returns early due to being an added load on the heart) • Blood pressure meter, Doppler US, piezoelectric receivers etc. may also be used to estimate PWV Elastography – commercial implementation • Increasing number of commercial systems now offer elastography: method gaining acceptance Example: • real-time elastography (RTE) of Hitachi Medical Systems • user applies continuous small (de)compressions with array • strain graph provides feedback to user of (de)compressions and shows region selected for generation of elastogram Real-time elastography showing hard circular inclusion. Left: grayscale B-mode with overlaid elastography color map. Right: grayscale B-mode. Bottom left: graph of strain with time, with red box showing region that was used to generate elastogram for maximum SNR. Image courtesy of Hitachi Medical Systems. http://hitachimedicalsystems.com/english/products/us/a vius/contents2.html [Alizad et al. 2006] In vivo breast vibro-acoustography: recent results and new challenges [Alizad et al. 2008] Image features in medical vibro-acoustography: In vitro and in vivo results [Baxter et al. 2001] Preventive health care, 2001 update: Should women be routinely taught breast self-examination to screen for breast cancer? http://www.ncbi.nlm.nih.gov/pmc/articles/PMC81191/?tool=pmcentrez [Bercoff et al. 2004] Monitoring thermally-induced lesions with supersonic shear imaging [Boutoyrie et al. 2009] Assessment of pulse wave velocity [Catheline et al. 2004] Measurement of viscoelastic properties of homogeneous soft solid using transient elastography: An inverse problem approach [Cobbold 2007] Foundations of biomedical ultrasound [Fahey et al. 2004] Acoustic radiation force impulse imaging of thermally-and chemically-induced lesions in soft tissues: preliminary ex vivo results ... ... [Foty and Steinberg 2005] The differential adhesion hypothesis: a direct evaluation [Gao et al. 1996] Imaging of the elastic properties of tissue – a review [Gyφngy 2010] Passive cavitation mapping for monitoring ultrasound therapy [Kennedy 2005] High-intensity focused ultrasound in the treatment of solid tumours [Kiss et al. 2004] Viscoelastic characterization of in vitro canine tissue [Konofagou 2004] Quo vadis elasticity imaging? [Larrat et al. 2010] MR-guided transcranial brain HIFU in small animal models [Lighthill 2005] Waves in fluids [Maleke and Konofagou 2008] Harmonic motion imaging for focused ultrasound (HMIFU): a fully integrated technique for sonication and monitoring of the thermal ablation in tissues [Nightingale et al. 2001] On the feasibility of remote palpation using acoustic radiation force ... ... [Nightingale et al. 2003] Shear-wave generation using acoustic radiation force: in vivo and ex vivo results [Parker et al. 2005] A unified view of imaging the elastic properties of tissue [Raichel 1972] Sound propagation in voigt fluid [Righetti et al. 1999] Elastographic characterization of HIFU-induced lesions in canine livers [Sarvazyan et al. 1998] Shear wave elasticity imaging: a new ultrasonic technology of medical diagnostics [Segers et al. 2009] Limitations and pitfalls of non-invasive measurement of arterial pressure wave reflections and pulse wave velocity [Stokes 1851] On the effect of the internal friction of fluids on the motion of pendulums [Szabo 1994] Time domain wave equations for lossy media obeying a frequency power law [Vappou et al. 2009] Quantitative viscoelastic parameters measured by harmonic motion imaging